Calculus Examples

$y = e^{\tan (θ)}$

Step 1

Differentiate using the chain rule, which states that $\frac{d}{d ?} [f (g (?))]$ is $f' (g (?)) g' (?)$ where $f (?) = ?^{\tan (θ)}$ and $g (?) = e$ .

Tap for more steps...

Step 1.1

To apply the Chain Rule, set $u$ as $e$ .

$\frac{d}{d u} [u^{\tan (θ)}] \frac{d}{d ?} [e]$

Step 1.2

Differentiate using the Power Rule which states that $\frac{d}{d u} [u^{n}]$ is $n u^{n - 1}$ where $n = \tan (θ)$ .

$\tan (θ) u^{\tan (θ) - 1} \frac{d}{d ?} [e]$

Step 1.3

Replace all occurrences of $u$ with $e$ .

$\tan (θ) e^{\tan (θ) - 1} \frac{d}{d ?} [e]$

Step 2

Since $e$ is constant with respect to $?$ , the derivative of $e$ with respect to $?$ is $0$ .

$\tan (θ) e^{\tan (θ) - 1} \cdot 0$

Step 3

Combine terms.

Tap for more steps...

Step 3.1

Multiply $0$ by $\tan (θ)$ .

$0 e^{\tan (θ) - 1}$

Step 3.2

Multiply $0$ by $e^{\tan (θ) - 1}$ .

$0$